224비트 소수체에서 효율적인 모듈러 곱셈
Efficient Modular Multiplication for 224-bit Prime Field
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참고문헌
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초록
타원곡선 상수배 연산은 사영좌표계를 기반으로 대부분 모듈러 곱셈으로 계산되므로 모듈러 곱셈의 효율성은 타원곡선암호의 성능에 크게 영향을 미친다. 본 논문에서는 FIPS 186-4의 224비트 소수체에서 효율적인 모듈러 곱셈방법을 제안한다. 제안하는 방법은 Karatsuba 곱셈과 새로운 모듈러 감산을 수행한다. 제안하는 모듈러 곱셈은 기존방법에 비하여 25%정도 빠르며, 모듈러 감산만 비교하면 기존 방법보다 50% 연산으로 계산이 가능하다.
Abstract
The performance of Elliptic Curves Cryptosystem(ECC) is dominated by the modular multiplication since the elliptic curvescalar multiplication consists of the modular multiplication in projective coordinates. In this paper, we propose a new methodthat combines the Karatsuba-Ofman multiplication method and a new modular reduction algorithm in order to improve theperformance of the modular multiplication for NIST p224 in the FIPS 186-4 standard. The proposed method leads to arunning time improvement for computing the modular multiplication about 25% faster than the previous methods. The resultsalso show that the method can reduce the arithmetic complexity by half when compared with traditional implementations onthe standpoint of the modular reduction.
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